In any digital communication system, and in particular in wireless communication systems, the receiver is equipped, amongst other things, with a detection mechanism and a frame start time estimation mechanism.
Detection is a well-known issue in the state of the art. It is an operation that consists in processing a signal received from a transmitter in order to determine if this signal is carrying useful information. Referring to FIG. 1, there is shown a receiver 1 receiving a signal that is also transmitted to a cost function F1 computation block 2. The result of the cost function is transmitted to a comparator 3 that compares this value with the value of a preset threshold K. The result of the comparison is then used, as represented in FIG. 2, to discriminate the signal from the noise and to activate receiver 1.
Consequently, threshold K is especially important since it directly determines the enabling of receiver 1. Moreover, the threshold affects the performance of the detector and in particular the probability of a detection error, be it false alarm (FA)—i.e. the detection of a signal whereas there is only noise—or a miss detection (absence of signal detection).
In a more formal way, let us adopt the following expression conventions:    H0: hypothetical case where there is only noise    H1: hypothetical case where both signal and noise are present    D0: hypothetical case where there is detection of noise only    D1: hypothetical case where there is detection of signal and noise
A traditionally used cost function consists in establishing a correlation between various samples of the received signal, the probability law of the cost function being different according to whether the hypothetical case H0 or H1 applies.
If one considers the characteristic curves of the probability density function of this cost function in the two possible cases (FIG. 3), the traditional method consists in setting a threshold K that will make it possible to decide between one and the other hypothesis. The probability of a detection error can then be written as follows:P[(D1,H0)∪(D0,H1)]=p(Fc>K,n)+p(Fc<K,s)
It can be shown that the intersection of both curves determines the value of an optimal threshold K that makes it possible to minimize the sum of the above terms. It is thus necessary, in the receiver, to adjust threshold K used in the mechanism of FIG. 1 in order to set its value to the optimal threshold because the threshold directly determines the performance of the detector. If a threshold is set too low the first term of the above equation will increase—i.e. the probability of false alarm—and, if the threshold is set too high, then the other term will increase, thus increasing the risk of signal miss detection. Only the optimal value, represented in FIG. 3, makes it possible to minimize the mathematical expression above thus ensuring to obtain detection with as few errors as possible.
In practice, the signal and noise probability density are not precisely known and thus the value of threshold K must be approximately set by empiric means.
As a result, the detector's performance is poor.
Moreover, It can be noted that threshold K directly affects the operation known as frame start time estimation, namely determining the exact moment when the signal becomes informative. Once the presence of a periodic signal has been detected, it is important to be able to identify the beginning of the frame. Such estimation must allow the receiver to precisely target the first symbols received from the transmitter. If threshold K is empirically set too low, then the receiver will have to manage a lot of false detections and, in the opposite case, the signal will not be detected anymore. Thus, the detection operation indeed has a direct influence on the estimation operation.
Therefore, with known techniques one is confronted with the insurmountable problem of having to precisely determine the threshold K to use in a detector. In practice, it is impossible to determine an optimal threshold because of the difficulty of knowing precisely the distribution laws and their characteristics in relation to the signal and noise in a concrete case. Then there is often no other option than to set threshold K in an empirical and approximate way, by studying the behavior of the channel.
This is the reason why, regarding detection or estimation, known receivers show limited performance whatever the particular technique employed: MC (Maximum Correlation), Minimum Mean Square Error (MMSE), SCHMIDL, for all these techniques start from the postulate that the threshold must be set to its optimal value. The problem common to all these techniques lies in the importance of appropriately setting the value of threshold K.
It would be desirable to find an alternative technique and to be freed from having to determine threshold K for carrying out detection and more generally for controlling a receiver in a digital communication system.